Abstract
In: http://arxiv.org/pdf/math/0609189v1.pdf, 2006
Online
academicJournal
Zugriff:
We study the propagation of orientation waves in a director field with rotational inertia and potential energy given by the Oseen-Frank energy functional from the continuum theory of nematic liquid crystals. There are two types of waves, which we call splay and twist waves. Weakly nonlinear splay waves are described by the quadratically nonlinear Hunter-Saxton equation. Here, we show that weakly nonlinear twist waves are described by a new cubically nonlinear, completely integrable asymptotic equation. This equation provides a surprising representation of the Hunter-Saxton equation for u as an advection equation for v, where uxx = v 2 x. There is an analogous representation of the Camassa-Holm equation. We use the asymptotic equation to analyze a one-dimensional initial value problem for the director-field equations with twist-wave initial data.
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Autor/in / Beteiligte Person: | John K. Hunter, B ; Consiglio Nazionale Delle Ricerche ; The Pennsylvania State University CiteSeerX Archives |
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Zeitschrift: | http://arxiv.org/pdf/math/0609189v1.pdf, 2006 |
Veröffentlichung: | 2006 |
Medientyp: | academicJournal |
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